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Author : M. Ishida
Publisher : Springer
ISBN 13 : 3540375538
Total Pages : 123 pages
Book Rating : 4.5/5 (43 download)
Download or read book The Genus Fields of Algebraic Number Fields written by M. Ishida and published by Springer. This book was released on 2006-12-08 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: a
Author : Makoto Ishida
Publisher : Springer
ISBN 13 : 9780387080000
Total Pages : 115 pages
Book Rating : 4.0/5 (8 download)
Download or read book The Genus Fields of Algebraic Number Fields written by Makoto Ishida and published by Springer. This book was released on 1976-01-01 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Makoto Ishida
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (64 download)
Download or read book The genus field of algebraic number fields written by Makoto Ishida and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Albrecht Fröhlich
Publisher :
ISBN 13 :
Total Pages : 724 pages
Book Rating : 4.3/5 (91 download)
Download or read book Algebraic Number Fields written by Albrecht Fröhlich and published by . This book was released on 1977 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Hilbert
Publisher : Springer Science & Business Media
ISBN 13 : 9783540627791
Total Pages : 402 pages
Book Rating : 4.6/5 (277 download)
Download or read book The Theory of Algebraic Number Fields written by David Hilbert and published by Springer Science & Business Media. This book was released on 1998-08-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Author : P E Conner
Publisher : World Scientific
ISBN 13 : 9814513520
Total Pages : 328 pages
Book Rating : 4.8/5 (145 download)
Download or read book A Survey Of Trace Forms Of Algebraic Number Fields written by P E Conner and published by World Scientific. This book was released on 1984-07-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every finite separable field extension F/K carries a canonical inner product, given by trace(xy). This symmetric K-bilinear form is the trace form of F/K.When F is an algebraic number field and K is the field Q of rational numbers, the trace form goes back at least 100 years to Hermite and Sylvester. These notes present the first systematic treatment of the trace form as an object in its own right. Chapter I discusses the trace form of F/Q up to Witt equivalence in the Witt ring W(Q). Special attention is paid to the Witt classes arising from normal extensions F/Q. Chapter II contains a detailed analysis of trace forms over p-adic fields. These local results are applied in Chapter III to prove that a Witt class X in W(Q) is represented by the trace form of an extension F/Q if and only if X has non-negative signature. Chapter IV discusses integral trace forms, obtained by restricting the trace form of F/Q to the ring of algebraic integers in F. When F/Q is normal, the Galois group acts as a group of isometries of the integral trace form. It is proved that when F/Q is normal of prime degree, the integral form is determined up to equivariant integral equivalence by the discriminant of F alone. Chapter V discusses the equivariant Witt theory of trace forms of normal extensions F/Q and Chapter VI relates the trace form of F/Q to questions of ramification in F. These notes were written in an effort to identify central problems. There are many open problems listed in the text. An introduction to Witt theory is included and illustrative examples are discussed throughout.
Author : Gerald J. Janusz
Publisher : American Mathematical Soc.
ISBN 13 : 0821804294
Total Pages : 288 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic Number Fields written by Gerald J. Janusz and published by American Mathematical Soc.. This book was released on 1996 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important theorems regarding the units of the ring of integers and the class group are proved and illustrated with many examples given in detail. The completion of an algebraic number field at a valuation is discussed in detail and then used to provide economical proofs of global results. The book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are provided to indicate applications of the general theory.
Author : Thomas Randle Butts
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.3/5 (129 download)
Download or read book On the Genus Field and Its Applications to Four Problems in Algebraic Number Theory written by Thomas Randle Butts and published by . This book was released on 1973 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P.M. Cohn
Publisher : CRC Press
ISBN 13 : 1351086480
Total Pages : 154 pages
Book Rating : 4.3/5 (51 download)
Download or read book Algebraic Numbers and Algebraic Functions written by P.M. Cohn and published by CRC Press. This book was released on 2018-01-18 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.
Author : Emil Artin
Publisher : American Mathematical Soc.
ISBN 13 : 0821840754
Total Pages : 366 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic Numbers and Algebraic Functions written by Emil Artin and published by American Mathematical Soc.. This book was released on 2005 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originated from the notes of a course given at Princeton University in 1950-1951, this text offers an introduction to algebraic numbers and algebraic functions. It starts with the general theory of valuation fields, proceeds to the local class field theory, and then to the theory of function fields in one variable.
Author : Harvey Cohn
Publisher : Springer Science & Business Media
ISBN 13 : 1461299500
Total Pages : 344 pages
Book Rating : 4.4/5 (612 download)
Download or read book A Classical Invitation to Algebraic Numbers and Class Fields written by Harvey Cohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Artin's 1932 Göttingen Lectures on Class Field Theory" and "Connections between Algebrac Number Theory and Integral Matrices"
Author : Daniel A. Marcus
Publisher : Springer
ISBN 13 : 3319902334
Total Pages : 213 pages
Book Rating : 4.3/5 (199 download)
Download or read book Number Fields written by Daniel A. Marcus and published by Springer. This book was released on 2018-07-05 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
Author : Wladyslaw Narkiewicz
Publisher : Springer Science & Business Media
ISBN 13 : 3662070014
Total Pages : 712 pages
Book Rating : 4.6/5 (62 download)
Download or read book Elementary and Analytic Theory of Algebraic Numbers written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Author : Zhang Xian Ke
Publisher : ALPHA SCIENCE INTERNATIONAL LIMITED
ISBN 13 : 1783323094
Total Pages : 416 pages
Book Rating : 4.7/5 (833 download)
Download or read book Algebraic Number Theory written by Zhang Xian Ke and published by ALPHA SCIENCE INTERNATIONAL LIMITED. This book was released on 2016-03-14 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: ALGEBRAIC NUMBER THEORY provides concisely both the fundamental and profound theory, starting from the succinct ideal theory (Chapters 1-3), turning then to valuation theory and local completion field (Chapters 4-5) which is the base of modern approach. After specific discussions on class numbers, units, quadratic and cyclotomic fields, and analytical theory (Chapters 6-8), the important Class Field Theory (Chapter 9) is expounded, and algebraic function field (Chapter 10) is sketched. This book is based on the study and lectures of the author at several universities.
Author :
Publisher : Academic Press
ISBN 13 : 0080873707
Total Pages : 233 pages
Book Rating : 4.0/5 (88 download)
Download or read book Algebraic Number Fields written by and published by Academic Press. This book was released on 1973-08-15 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Number Fields
Author : David Hilbert
Publisher : Springer Science & Business Media
ISBN 13 : 3662035456
Total Pages : 360 pages
Book Rating : 4.6/5 (62 download)
Download or read book The Theory of Algebraic Number Fields written by David Hilbert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Author : Gabriel Daniel Villa Salvador
Publisher : Springer Science & Business Media
ISBN 13 : 0817645152
Total Pages : 658 pages
Book Rating : 4.8/5 (176 download)
Download or read book Topics in the Theory of Algebraic Function Fields written by Gabriel Daniel Villa Salvador and published by Springer Science & Business Media. This book was released on 2007-10-10 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.
